Abstract

We report the investigation of conductance fluctuation and shot noise in disordered graphenesystems with two kinds of disorder, Anderson type impurities and random dopants. To avoid the traditional exact but time-consuming approach, known as brute-force calculation, which is somehow impractical at low doping concentration, we develop an expansion method based on the coherent potential approximation (CPA) to calculate the average of four Green's functions, and the results are obtained by truncating the expansion up to 6th order in terms of “single-site-T-matrix.” Since our expansion is with respect to “single-site-T-matrix” instead of disorder strength W, good result can be obtained at 6th order for finite W. We benchmark our results against brute-force method on disordered graphenesystems as well as the two dimensional square lattice model systems for both Anderson disorder and the random doping. The results show that in the regime where the disorder strength W is small or the doping concentration is low, our results agree well with the results obtained from the brute-force method. Specifically, for the graphenesystem with Anderson impurities, our results for conductance fluctuation show good agreement for W up to 0.4t, where t is the hopping energy. While for average shot noise, the results are good for W up to 0.2t. When the graphenesystem is doped with low concentration 1%, the conductance fluctuation and shot noise agrees with brute-force results for large W which is comparable to the hopping energy t. At large doping concentration 10%, good agreement can be reached for conductance fluctuation and shot noise for W up to 0.4t. We have also tested our formalism on square lattice with similar results. Our formalism can be easily combined with linear muffin-tin orbital first-principles transport calculations for light doping nano-scaled systems, making prediction on variability of nano-devices.

Received 30 May 2013Accepted 25 July 2013Published online 09 August 2013

Acknowledgments:

The authors would like to thank L. Zhang, G. B. Liu, Y. Wang, Y. Zhu, and H. Guo for their helpful discussions. We gratefully acknowledge the support from Research Grant Council (HKU 705611P) and University Grant Council (Contract No. AoE/P-04/08) of the Government of HKSAR. This research is conducted using the HKU Computer Centre research computing facilities that are supported in part by the Hong Kong UGC Special Equipment Grant (SEG HKU09).